In Chile, a vast and persistent gender gap in math performance at university admission has negative consequences for women's opportunities. International evidence suggests that these gender differences reflect gender inequities in educational and economic opportunities available in a given culture. A theoretical model suggests that sociocultural factors such as gender stereotype and math anxiety have an impact on women's math abilities by affecting their skills for cognitive reflection. This cross-sectional study collected data from 259 university students to gather preliminary evidence on the close relationship between gender gaps in math achievement and gender gaps in cognitive reflection. A mediation analysis shows that the level of cognitive reflection of students fully mediates the effect of gender on math achievement, even after controlling for participants' linguistic abilities. These findings support the possibility that there is a close relationship between gender differences in cognitive reflection and gender gaps in math achievement at university admission in Chile. The discussion emphasizes that the university admission's data is under the control of state agencies with strict protocols of information access that undermines the feasibility of researching this area. Assessments of cognitive reflection are easy to administer in only a few minutes and under laboratory conditions. Hence, one way to boost the viability of research and diagnosis of gender gaps in Chile is to use cognitive reflection assessments as proximal estimates for gender gaps in math performance at university admission.